Simplify; express your answer in exponential form. Assume $x\neq 0, q\neq 0$. $\dfrac{{x^{4}}}{{(x^{2}q^{2})^{3}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${x^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${x^{4} = x^{4}}$ In the denominator, we can use the distributive property of exponents. ${(x^{2}q^{2})^{3} = (x^{2})^{3}(q^{2})^{3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{x^{4}}}{{(x^{2}q^{2})^{3}}} = \dfrac{{x^{4}}}{{x^{6}q^{6}}}$ Break up the equation by variable and simplify. $\dfrac{{x^{4}}}{{x^{6}q^{6}}} = \dfrac{{x^{4}}}{{x^{6}}} \cdot \dfrac{{1}}{{q^{6}}} = x^{{4} - {6}} \cdot q^{- {6}} = x^{-2}q^{-6}$.